Back to the Roots of Vector and Tensor Calculus. Heaviside versus Gibbs

TL;DR

This paper explores the historical influence of Gibbs's vector analysis on Heaviside, analyzing annotations to understand their intellectual relationship and impact on the development of vector and tensor calculus.

Contribution

It provides a detailed analysis of Heaviside's annotations on Gibbs's unpublished pamphlet, revealing the influence of Gibbs's work on Heaviside's development of vector calculus.

Findings

Heaviside studied Gibbs's work carefully and annotated his pamphlet.

Heaviside defended Gibbs's vector analysis against quaternionists.

Gibbs's work significantly influenced Heaviside's development of vector calculus.

Abstract

In June 1888, Oliver Heaviside received by mail an officially unpublished pamphlet, which was written and printed by the American author Willard J. Gibbs around 1881-1884. This original document is preserved in the Dibner Library of the History of Science and Technology at the Smithsonian Institute in Washington DC. Heaviside studied Gibbs's work very carefully and wrote some annotations in the margins of the booklet. He was a strong defender of Gibbs's work on vector analysis against quaternionists, even if he criticized Gibbs's notation system. The aim of our paper is to analyse Heaviside's annotations and to investigate the role played by the American physicist in the development of Heaviside's work.